A hyperbolic Stefan problem based on the linearized Gurtin{Pipkin heat conduction law is considered. Temperature and free boundary are controlled by a thermostat acting on the boundary. This feedback control is based on temperature measurements performed by real thermal sensors located into the domain containing the two{phase system and/or at its boundary. Three di erent types of thermostats ar...

Salva and Tarzia, [N.N. Salva, D.A. Tarzia, J. Math. Anal. Appl. 379 (2011) 240 244], gave explicit solutions of a similarity type for a class of free boundary problem for a semi-infinite material. In this paper, through an elementary approach and less stringent assumption on data, we obtain more general results than those given by their central result, and thereby construct explicit solutions ...

In this paper we consider one-dimensional two-phase Stefan problems for a class of parabolic equations with nonlinear heat source terms and with nonlinear flux conditions on the fixed boundary. Here, both timedependent and time-independent source terms and boundary conditions are treated. We investigate the large time behavior of solutions to our problems by using the theory for dynamical syste...